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The phrase "an argument based on" is correct and usable in written English.
You can use it when discussing the foundation or reasoning behind a particular argument or claim.
Example: "The author presents an argument based on empirical evidence to support her thesis."
Alternatives: "a claim grounded in" or "a rationale derived from".
Exact(60)
A common method is to estimate σ2 while minimizing the false positive rate (Pfa) via an argument based on leave-one-out cross validation [11, 22 25], which gives the following upper bound on Pfa: (6).
A second possible explanation for the apparent disagreement between experiment and simulation would be based on refuting the single-structure-based interpretation of the NMR data, and on evoking an argument based on averaging between distinct and fast-interconverting peptide structures.
(This can be established rigorously with an argument based on random sampling of gametes, analogous to the argument used in the one-locus case).
"Such an argument, based on a sound scientific basis, has not been made..
The first prong, he said, would be an argument based on the Clean Air Act authority.
In response, Google has advanced an argument based on editorial integrity.
Justice Wiggins responded to the campaign with an argument based on civics.
You should make an argument based on your analysis of the sources.
In addition, more and more, Mr. Rangel and other Democratic leaders are making an argument based on race.
This is now no longer an argument based on fear but on the law of the land.
Clinton has a majority of the pledged delegates as well, so there isn't really an argument based on electoral returns.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com